Strictly proper 7-note 31edo scales

Below are listed scales which are strictly proper, in the sense the term is used by music theorist David Rothenberg. The "type" of a scale is defined by the linear temperament supported by 31et in which it has the least span. "Breed type" means it is a tie between miracle and hemiwuerschmidt.

Meantone type

schema	name	example(s)
5535553	Meantone[7]; diatonic scale
5355553	Melodic minor scale
5355373	Harmonic minor scale; inverse harmonic major
5535373	Harmonic major scale; inverse harmonic minor
5533555	Major locrian scale
3717355	Diminished diatonic scale	Strange Diatonic by Chris Vaisvil play Omega centauri by Zach Curley
5535643	Enharmonic major; inverse enharmonic minor
5346535	Enharmonic minor; inverse enharmonic major
5535625	Enharmonic mixolydian
5526535	Inverse enharmonic mixolydian
5526355	Enharmonic major-minor
5553625	Inverse enharmonic major-minor
6435625	Major doubleflat; inverse minor doubleflat
5346526	Minor doubleflat; inverse major doubleflat
5553652	Ping
3555256	Inverse ping
3726355	Alhijaz; inverse ambika
6273553	Ambika; inverse alhijaz
6453652	Kung; inverse ousak
3546256	Ousak; inverse kung

Valentine

6446272	Silver
6444472	Harmonia
4446274	Inverse harmonia
6444562	Pendragon
4626544	Inverse pendragon
6264463	Hipop
4626364	Inverse Hipop
4626445	Malakon
4626454	Inverse malakon
4464526	Bagpipe
4644625	Inverse bagpipe
6444625	Pitu
6444652	Inverse pitu
6444445	Porch
4446544	Inverse porch

Miracle type

5436346	Subdom scale; inverse superton
5643634	Superton scale; inverse subdom
5436364	Nudia; neutral diatonic
5463634	Inverse nudia
3636346	Nurow; Neutral triads in row
6363643	Inverse nurow

Mohajira type

4554454	Sikah; Rast; Neutral Diatonic Hypolydian
4444555	Sheimanic
4554445	Thaiic
4544455	Inverse thaiic
4545454	Mohajira; Neutral Dorian

Hemiwuerschmidt type

5555515	Hemiwuerschmidt/Hemithirds[7]
5544652	Hemaj; inverse hemin
4455256	Hemin; inverse hemaj
4525546	Gypsi; 11/9-10/7-7/4 chord on tonic
4552546	Inverse gypsi; 11/9-10/7-7/4 chord on tonic
5555542	Leadhole
5555524	Inverse leadhole

Mothra type

5553643	Lydic
5553463	Inverse lydic
5535463	Ionic
5364535	Aeolic; inverse ionic
4644463	Quahog
6444643	Inverse quahog
6453643	Higasi
4635463	Inverse higasi

Orwell type

5364463	Orminor
4644643	Ormed
4644364	Augton
4644634	Inverse augton

Breed type

3456265	Hemisub
4356265	Inverse hemisub
6354535	Heminewt
4536535	Inverse heminewt